Wave Seminar : A remark on Rellich’s theorem

2015-11-9 16:30 - 2015-11-9 18:00
Faculty of Science Building #3, Room 309
Kenichi Ito (Kobe University)
We consider the Schr\"odinger operator on a manifold with Euclidean and/or hyperbolic ends, and discuss the maximal exponential decay rates for generalized eigenfunctions associated with complex eigenvalues. The proof depends on a variation of the Mourre commutator argument. In the latter part of talk we mention the asymptotic behaviors of $B_0^*$-eigenfucntions associated with real eigenvalues above a critical energy, and also their relations to the scattering matrix.
This talk is based on a joint work with Erik Skibsted, Aarhus University.